New applications of the Muntz and Coffman algorithm

Abstract

SUMMARYMuntz and Co man proposed an algorithm to solve the problem of scheduling preemptable tasks either with arbitrary precedences on two processors, or tasks with tree-like precedences on an arbitrary number of processors, for the schedule length criterion. In this work, we demonstrate that this well-known algorithm has interesting features which extend its application to many other scheduling problems. Three deterministic scheduling problems for preemptable tasks are considered. Though these problems have diverse formulations, they have at least one thing in common: Basically their optimization algorithms boil down to the Muntz-Co man algorithm. The foundations of the Muntz-Co man algorithm versatility are established.

Minimizing Weighted Mean Completion Time for Malleable Tasks Scheduling

“…In the clairvoyant case, most of scheduling problems for independent malleable work-preserving tasks are polynomially solvable when the goal is to minimize the makespan. For instance, P |var; V i /q, δ i , r i |C max (even in presence of release dates r i s) can be solved in time O(n 2 ) [10]. The maximum lateness problem P |var; V i /q, δ i , r i |L max is also solvable in time O(n 4 P ) [2].…”